What’s the fastest way to find the highest common factor (HCF) of two numbers — and how can you check your answer?

The most efficient method is:

  1. Find all the factors of the smaller number.
  2. Check, from largest to smallest, which of these also divides the larger number exactly.

As soon as one does — that’s your HCF.

Let’s walk through an example.

HCF of 16 and 40

Step-by-step:

  • Smaller number is 16.

  • Factors of 16: $[1, 2, 4, 8, 16]$

  • Check from largest down:

    • $40 \div 16 = 2.5$ → ❌
    • $40 \div 8 = 5$ → ✅

So the highest common factor is:

$$ \boxed{8} $$

How To Check Your Answer

Now reverse it by checking the factors of the larger number.

  • Larger number is 40.

  • Factors of 40: $[1, 2, 4, 5, 8, 10, 20, 40]$

  • Eliminate those greater than 16: $[1, 2, 4, 5, 8, 10]$

  • Check from largest down:

    • $16 \div 10 = 1.6$ → ❌
    • $16 \div 8 = 2$ → ✅

Same result. The HCF is:

$$ \boxed{8} $$

Summary

The highest common factor (HCF) of 16 and 40 is:

$$ \boxed{8} $$

This is the largest number that divides both 16 and 40 with no remainder.
Knowing how to find the HCF is especially helpful when simplifying fractions or solving arithmetic problems efficiently.